
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import tensorflow as tf
plt.rcParams['figure.figsize'] = [12, 6]
plt.rcParams.update({'font.size': 12})


df = pd.read_excel('columns.xlsx')
col = df['Symbol'].values
col = col.tolist()


df_stableFeedFlow = pd.read_csv(r'https://raw.githubusercontent.com/AshuPraja13/FCC-abnormality-detection/main/NOC_stableFeedFlow_outputs.csv',header=None)
df_stableFeedFlow.set_index = df_stableFeedFlow.iloc[:,0]
df_stableFeedFlow = df_stableFeedFlow.drop(columns=0)
df_stableFeedFlow.columns= col
df_stableFeedFlow.sample(5)


df_varyingFeedFlow=pd.read_csv(r'https://raw.githubusercontent.com/AshuPraja13/FCC-abnormality-detection/main/NOC_varyingFeedFlow_outputs.csv',header=None)
df_varyingFeedFlow.set_index = df_varyingFeedFlow.iloc[:,0]
df_varyingFeedFlow = df_varyingFeedFlow.drop(columns=0)
df_varyingFeedFlow.columns= col
df_varyingFeedFlow.sample(5)


df_UAf_decrease = pd.read_csv(r'https://raw.githubusercontent.com/AshuPraja13/FCC-abnormality-detection/main/UAf_decrease_outputs.csv',header=None)
df_UAf_decrease.set_index = df_UAf_decrease.iloc[:,0]
df_UAf_decrease = df_UAf_decrease.drop(columns=0)
df_UAf_decrease.columns= col
df_UAf_decrease.sample(5)


df_UAf_decrease.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1440 entries, 0 to 1439
Data columns (total 46 columns):
 #   Column       Non-Null Count  Dtype  
---  ------       --------------  -----  
 0   F3           1440 non-null   float64
 1   Tatm         1440 non-null   float64
 2   T1           1440 non-null   float64
 3   P4           1440 non-null   float64
 4   deltaP       1440 non-null   float64
 5   P6           1440 non-null   int64  
 6   Fair         1440 non-null   float64
 7   T3           1440 non-null   float64
 8   T2           1440 non-null   float64
 9   Tr           1440 non-null   float64
 10  Treg         1440 non-null   float64
 11  Lsp          1440 non-null   float64
 12  Tcyc         1440 non-null   float64
 13  Tcyc - Treg  1440 non-null   float64
 14  Cco,sg       1440 non-null   int64  
 15  Co2,sg       1440 non-null   float64
 16  P5           1440 non-null   float64
 17  V4           1440 non-null   float64
 18  V6           1440 non-null   float64
 19  V7           1440 non-null   float64
 20  V3           1440 non-null   float64
 21  V1           1440 non-null   float64
 22  V2           1440 non-null   float64
 23  Frgc         1440 non-null   int64  
 24  Fsc          1440 non-null   int64  
 25  ACAB         1440 non-null   float64
 26  AWGC         1440 non-null   float64
 27  F5           1440 non-null   float64
 28  F7           1440 non-null   float64
 29  Fsg          1440 non-null   float64
 30  FV11         1440 non-null   int64  
 31  P1           1440 non-null   float64
 32  P2           1440 non-null   float64
 33  FLPG         1440 non-null   float64
 34  FLN          1440 non-null   float64
 35  FHN          1440 non-null   float64
 36  FLCO         1440 non-null   float64
 37  FSlurry      1440 non-null   float64
 38  FReflux      1440 non-null   float64
 39  Tfra         1440 non-null   float64
 40  T10          1440 non-null   float64
 41  T20          1440 non-null   float64
 42  V9           1440 non-null   float64
 43  V8           1440 non-null   float64
 44  V10          1440 non-null   float64
 45  V11          1440 non-null   float64
dtypes: float64(41), int64(5)
memory usage: 517.6 KB


df_UAf_decrease.describe().T


sns.heatmap(df_UAf_decrease.corr(),cmap='coolwarm')

<AxesSubplot:>


for n,i in enumerate(df_stableFeedFlow.columns):
    plt.figure(figsize=(12,2))
    plt.plot(df_stableFeedFlow[i])
    plt.xlabel('time (mins)')
    plt.ylabel(i)
    plt.title(df[df['Symbol']==i]['Description'].values)
    plt.show()


for n,i in enumerate(df_varyingFeedFlow.columns):
    plt.figure(figsize=(12,2))
    plt.plot(df_varyingFeedFlow[i])
    plt.xlabel('time (mins)')
    plt.ylabel(i)
    plt.title(df[df['Symbol']==i]['Description'].values)
    plt.show()


for n,i in enumerate(df_UAf_decrease.columns):
    plt.figure(figsize=(12,2))
    plt.plot(df_UAf_decrease[i])
    plt.xlabel('time (mins)')
    plt.ylabel(i)
    plt.title(df[df['Symbol']==i]['Description'].values)
    plt.show()


from sklearn.preprocessing import StandardScaler
ss = StandardScaler()


X = ss.fit_transform(df_stableFeedFlow)


from sklearn.decomposition import PCA
pca = PCA()


X_pca = pca.fit_transform(X)


plt.figure(figsize=(15,6))
sns.set_style('whitegrid')
sns.lineplot(x=list(range(1,47)), y=np.cumsum(pca.explained_variance_ratio_), drawstyle='steps-pre')
sns.lineplot(x=list(range(0,46)),y=np.cumsum(pca.explained_variance_ratio_))
plt.xlabel('Eigen Values')
plt.ylabel('Ratio of Variance')
plt.title('Variance by each Eigen Value')
plt.show()


pca = PCA(n_components=10)
X_pca = pca.fit_transform(X)


plt.figure(figsize=(15,6))
sns.set_style('whitegrid')
sns.lineplot(x=list(range(1,11)), y=np.cumsum(pca.explained_variance_ratio_), drawstyle='steps-pre')
sns.lineplot(x=list(range(0,10)),y=np.cumsum(pca.explained_variance_ratio_))
plt.xlabel('Eigen Values')
plt.ylabel('Ratio of Variance')
plt.title('Variance by each Eigen Value')
plt.show()


X_train = X.reshape(2880,46,1)


model = tf.keras.models.Sequential()
model.add(tf.keras.layers.Bidirectional(tf.keras.layers.LSTM(256,return_sequences=True),input_shape=(46,1)))
model.add(tf.keras.layers.Dropout(0.2))
model.add(tf.keras.layers.Bidirectional(tf.keras.layers.LSTM(128,return_sequences=True)))
model.add(tf.keras.layers.Dropout(0.2))
model.add(tf.keras.layers.Dense(1))
model.compile(optimizer='adam', loss='mse', metrics=['mae'])
model.summary()

Model: "sequential"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 bidirectional (Bidirection  (None, 46, 512)           528384    
 al)                                                             
                                                                 
 dropout (Dropout)           (None, 46, 512)           0         
                                                                 
 bidirectional_1 (Bidirecti  (None, 46, 256)           656384    
 onal)                                                           
                                                                 
 dropout_1 (Dropout)         (None, 46, 256)           0         
                                                                 
 dense (Dense)               (None, 46, 1)             257       
                                                                 
=================================================================
Total params: 1185025 (4.52 MB)
Trainable params: 1185025 (4.52 MB)
Non-trainable params: 0 (0.00 Byte)
_________________________________________________________________


model.fit(X_train,X_train,epochs=30)

Epoch 1/30
90/90 [==============================] - 90s 430ms/step - loss: 0.1571 - mae: 0.2174
Epoch 2/30
90/90 [==============================] - 39s 439ms/step - loss: 0.0030 - mae: 0.0381
Epoch 3/30
90/90 [==============================] - 39s 434ms/step - loss: 0.0025 - mae: 0.0342
Epoch 4/30
90/90 [==============================] - 39s 435ms/step - loss: 0.0023 - mae: 0.0321
Epoch 5/30
90/90 [==============================] - 40s 444ms/step - loss: 0.0021 - mae: 0.0305
Epoch 6/30
90/90 [==============================] - 39s 437ms/step - loss: 0.0019 - mae: 0.0292
Epoch 7/30
90/90 [==============================] - 39s 433ms/step - loss: 0.0019 - mae: 0.0285
Epoch 8/30
90/90 [==============================] - 40s 441ms/step - loss: 0.0018 - mae: 0.0278
Epoch 9/30
90/90 [==============================] - 40s 440ms/step - loss: 0.0017 - mae: 0.0275
Epoch 10/30
90/90 [==============================] - 40s 441ms/step - loss: 0.0017 - mae: 0.0268
Epoch 11/30
90/90 [==============================] - 39s 437ms/step - loss: 0.0017 - mae: 0.0267
Epoch 12/30
90/90 [==============================] - 40s 440ms/step - loss: 0.0016 - mae: 0.0262
Epoch 13/30
90/90 [==============================] - 39s 437ms/step - loss: 0.0016 - mae: 0.0261
Epoch 14/30
90/90 [==============================] - 39s 439ms/step - loss: 0.0016 - mae: 0.0258
Epoch 15/30
90/90 [==============================] - 40s 440ms/step - loss: 0.0015 - mae: 0.0256
Epoch 16/30
90/90 [==============================] - 39s 435ms/step - loss: 0.0015 - mae: 0.0253
Epoch 17/30
90/90 [==============================] - 39s 439ms/step - loss: 0.0015 - mae: 0.0253
Epoch 18/30
90/90 [==============================] - 39s 436ms/step - loss: 0.0015 - mae: 0.0250
Epoch 19/30
90/90 [==============================] - 39s 433ms/step - loss: 0.0015 - mae: 0.0251
Epoch 20/30
90/90 [==============================] - 40s 445ms/step - loss: 0.0015 - mae: 0.0250
Epoch 21/30
90/90 [==============================] - 43s 472ms/step - loss: 0.0014 - mae: 0.0247
Epoch 22/30
90/90 [==============================] - 40s 445ms/step - loss: 0.0014 - mae: 0.0247
Epoch 23/30
90/90 [==============================] - 40s 441ms/step - loss: 0.0014 - mae: 0.0247
Epoch 24/30
90/90 [==============================] - 40s 446ms/step - loss: 0.0014 - mae: 0.0246
Epoch 25/30
90/90 [==============================] - 40s 440ms/step - loss: 0.0014 - mae: 0.0245
Epoch 26/30
90/90 [==============================] - 25s 275ms/step - loss: 0.0014 - mae: 0.0247
Epoch 27/30
90/90 [==============================] - 24s 272ms/step - loss: 0.0014 - mae: 0.0242
Epoch 28/30
90/90 [==============================] - 24s 272ms/step - loss: 0.0014 - mae: 0.0242
Epoch 29/30
90/90 [==============================] - 24s 271ms/step - loss: 0.0014 - mae: 0.0245
Epoch 30/30
90/90 [==============================] - 25s 272ms/step - loss: 0.0014 - mae: 0.0244

<keras.src.callbacks.History at 0x205d50a2700>


error_ae = []
for i in range(X.shape[0]):
    y_pred = model.predict(X[i].reshape(1,46,1),verbose=None)[0,:,0]
    error_ae.append(np.abs(X[i]-y_pred).sum())
AE_CL = np.percentile(error_ae,99)


pd.Series(error_ae).plot()
plt.hlines(AE_CL,0,len(error_ae),colors='red',linestyles='--')

<matplotlib.collections.LineCollection at 0x205d52ad130>


X_reconstructed = np.dot(X_pca,pca.components_)
error_pca = X-X_reconstructed
Q_train = np.sum(np.abs(error_pca),axis=1)
Q_CL = np.percentile(Q_train,99)
# Q_train plot with CL
plt.figure()
plt.plot(Q_train, color='black')
plt.plot([1,len(Q_train)],[Q_CL,Q_CL], linestyle='--',color='red', linewidth=2)
plt.xlabel('Sample #')
plt.ylabel('Q metric: training data')
plt.title(f'Q metrix is max: {Q_train.max()} at:{Q_train.argmax()}mins')
plt.show()


lambda_ = np.diag(pca.explained_variance_)
lambda_inv = np.linalg.inv(lambda_)
T_train = np.zeros(X_pca.shape[0])
for i in range(X_pca.shape[0]):
    T_train[i] = np.dot(np.dot(X_pca[i],lambda_inv),X_pca[i].T)
T_CL = np.percentile(T_train,99)
# T2_train plot with CL
plt.figure()
plt.plot(T_train, color='black')
plt.plot([1,len(T_train)],[T_CL,T_CL], linestyle='--',color='red', linewidth=2)
plt.xlabel('Sample #')
plt.ylabel('T$^2$ metric: training data')
plt.title(f'T$^2$ metrix is max: {np.array(T_train).max()} at:{np.array(T_train).argmax()}mins')
plt.show()


cosine = []
ed = []
for i in range(X.shape[0]):
    v1 = X[i]
    v2 = np.dot(X_pca,pca.components_)[i]
    cosine.append(np.dot(v1,v2)/(np.linalg.norm(v1)*np.linalg.norm(v2)))
    ed.append(np.linalg.norm(v1 - v2))
C_CL = np.min(cosine)
E_CL = np.percentile(ed,99)
# pd.Series(ed).plot(color='black')
# plt.plot([1,len(ed)],[E_CL,E_CL], linestyle='--',color='red', linewidth=2)
# plt.show()
pd.Series(cosine).plot(color='black')
plt.plot([1,len(cosine)],[C_CL,C_CL], linestyle='--',color='red', linewidth=2)
plt.xlabel('Sample #')
plt.ylabel('Cosine similarity metric: training data')
plt.title(f'Cosine Similarity')
plt.show()


Q_CL,T_CL,C_CL,E_CL,AE_CL

(4.1231132155190835,
 20.4243503525688,
 0.9427550112367161,
 0.9281694746755801,
 0.37931151220578185)


def Q_test(X,X_pca,pca_components_,Q_CL):
    X_reconstructed = np.dot(X_pca,pca_components_)
    error_pca = X-X_reconstructed
    Q_train = np.sum(np.abs(error_pca),axis=1)
    # Q_train plot with CL
    plt.figure()
    plt.plot(Q_train, color='black')
    plt.plot([1,len(Q_train)],[Q_CL,Q_CL], linestyle='--',color='red', linewidth=2)
    plt.xlabel('Sample #')
    plt.ylabel('Q metric: training data')
    plt.title(f'Q metrix is max: {Q_train.max()} at:{Q_train.argmax()}mins')
    plt.show()
    return error_pca


def T_test(X_pca,explained_variance_,TCL):
    lambda_ = np.diag(pca.explained_variance_)
    lambda_inv = np.linalg.inv(lambda_)
    T_train = np.zeros(X_pca.shape[0])
    for i in range(X_pca.shape[0]):
        T_train[i] = np.dot(np.dot(X_pca[i],lambda_inv),X_pca[i].T)
    # T2_train plot with CL
    plt.figure()
    plt.plot(T_train, color='black')
    plt.plot([1,len(T_train)],[T_CL,T_CL], linestyle='--',color='red', linewidth=2)
    plt.xlabel('Sample #')
    plt.ylabel('T$^2$ metric: training data')
    plt.title(f'T$^2$ metrix is max: {np.array(T_train).max()} at:{np.array(T_train).argmax()}mins')
    plt.show()


def cosine(X,X_transformed,pca_components_,C_CL,E_CL):
    cosine = []
    ed = []
    for i in range(X.shape[0]):
        v1 = X[i]
        v2 = np.dot(X_transformed,pca_components_)[i]
        cosine.append(np.dot(v1,v2)/(np.linalg.norm(v1)*np.linalg.norm(v2)))
        ed.append(np.linalg.norm(v1 - v2))
#     pd.Series(ed).plot(color='black')
#     plt.plot([1,len(ed)],[E_CL,E_CL], linestyle='--',color='red', linewidth=2)
#     plt.xlabel('Sample #')
#     plt.ylabel('Eucledian Distance metric: training data')
#     plt.show()
    pd.Series(cosine).plot(color='black')
    plt.plot([1,len(cosine)],[C_CL,C_CL], linestyle='--',color='red', linewidth=2)
    plt.xlabel('Sample #')
    plt.ylabel('Cosine similarity metric: training data')
    plt.title(f'Cosine Similarity')
    plt.show()


def autoencoder(df_test,CL):
    X_test = ss.transform(df_test)
    error_ae = []
    error_sum = []
    for i in range(X_test.shape[0]):
        y_pred = model.predict(X_test[i].reshape(1,46,1),verbose=None)[0,:,0]
        error_ae.append(np.abs(X_test[i]-y_pred))
        error_sum.append(np.abs(X_test[i]-y_pred).sum())
    error_ae=np.array(error_ae)
    pd.Series(error_sum).plot(color = 'black')
    plt.hlines(CL,0,len(error_ae),colors='red',linestyles='--')
    plt.xlabel('Sample #')
    plt.ylabel('Reconstruction error by Autoencoder')
    return error_ae


X = ss.transform(df_varyingFeedFlow)
X_test = pca.transform(X)


error_pca = Q_test(X,X_test,pca.components_,Q_CL)


T_test(X_test,pca.explained_variance_,T_CL)


cosine(X,X_test,pca.components_,C_CL,E_CL)


error_ae = autoencoder(df_varyingFeedFlow,AE_CL)


X = ss.transform(df_UAf_decrease)
X_test = pca.transform(X)


error_pca = Q_test(X,X_test,pca.components_,Q_CL)


T_test(X_test,pca.explained_variance_,T_CL)


cosine(X,X_test,pca.components_,C_CL,E_CL)


error_ae = autoencoder(df_UAf_decrease,AE_CL)


#%% Q contribution
error = np.abs(error_pca).sum(axis=1)
cum = []
for index,value in enumerate(error):
    if (value>Q_CL) and (len(cum)<15):
        previous_val = value
        cum.append(value)
        if len(cum) == 15:
            sample = index
            break
    else:
        cum=[]
# sample = ((pd.Series(error_pca.sum(axis=1))-pd.Series(error_pca.sum(axis=1)).shift()).abs()).argmax()
print('Time-',sample,'mins')
error_test_sample = error_pca[sample]
Q_contri = np.abs(error_test_sample) # *error_test_sample # vector of contributions

Time- 200 mins


plt.figure(figsize=[15,4])
plt.bar(['variable ' + str((i+1)) for i in range(len(Q_contri))], Q_contri)
plt.xticks(rotation = 80)
plt.ylabel('Q contributions')
plt.show()


plt.figure(figsize=(15,40))
print('Time-',sample,'mins')
for i,n in enumerate(np.argsort(Q_contri)[:-11:-1]):
    plt.subplot(5,2,i+1)
    plt.plot(df_UAf_decrease.iloc[:,n],'blue', linewidth=1)
    plt.xlabel('time (mins)')
    plt.ylabel(df['Symbol'][n])
    plt.title(df['Description'][n])
    plt.show

Time- 200 mins


#%% Autoencoder Error
error = np.abs(error_ae).sum(axis=1)
cum = []
for index,value in enumerate(error):
    if (value>AE_CL) and (len(cum)<15):
        previous_val = value
        cum.append(value)
        if len(cum) == 15:
            sample = index
            break
    else:
        cum=[]
# sample = ((pd.Series(error_ae.sum(axis=1))-pd.Series(error_ae.sum(axis=1)).shift()).abs()).argmax()
print('Time-',sample,'mins')
error_test_sample = error_pca[sample]
Q_contri = np.abs(error_test_sample) # *error_test_sample # vector of contributions

Time- 349 mins


plt.figure(figsize=(15,45))
print('Time-',sample,'mins')
for i,n in enumerate(np.argsort(error_ae[sample])[:-11:-1]):
    plt.subplot(5,2,i+1)
    plt.plot(df_UAf_decrease.iloc[:,n],'blue', linewidth=1)
    plt.xlabel('time (mins)')
    plt.ylabel(df['Symbol'][n])
    plt.title(df['Description'][n])
    plt.show

Time- 349 mins

	F3	Tatm	T1	P4	deltaP	P6	Fair	T3	T2	Tr	...	FLCO	FSlurry	FReflux	Tfra	T10	T20	V9	V8	V10	V11
2141	164.85	79.997	460.82	34.4	-6.4	28	2.6781	1563.6	615.99	969.01	...	1635.2	217.39	2978.9	314.56	509.64	627.94	46.200	49.422	49.215	46.754
1777	165.17	78.614	460.93	34.4	-6.4	28	2.6840	1564.9	616.00	969.01	...	1650.0	212.13	3021.4	314.34	510.11	628.55	46.630	50.169	49.832	47.557
875	165.02	79.799	460.66	34.4	-6.4	28	2.6791	1565.7	616.00	968.97	...	1641.4	215.33	2997.2	314.74	509.80	628.14	46.061	49.697	49.492	47.094
2595	165.10	78.189	460.62	34.4	-6.4	28	2.6808	1566.4	616.00	968.98	...	1645.3	211.07	2982.3	313.39	509.85	628.12	47.687	49.677	49.167	47.313
1238	165.22	77.345	460.29	34.4	-6.4	28	2.6841	1569.1	616.00	969.00	...	1648.0	211.18	2994.5	313.09	510.02	628.40	48.189	49.933	49.413	47.450

	F3	Tatm	T1	P4	deltaP	P6	Fair	T3	T2	Tr	...	FLCO	FSlurry	FReflux	Tfra	T10	T20	V9	V8	V10	V11
2162	165.90	80.044	461.00	34.4	-6.4	28	2.6932	1569.1	616.01	968.98	...	1648.3	210.22	3100.7	316.65	510.68	629.28	44.175	51.092	49.450	47.405
2590	164.54	78.226	461.75	34.4	-6.4	28	2.6726	1556.1	616.01	968.99	...	1638.2	213.61	2908.8	312.10	509.21	627.18	48.963	48.667	48.967	46.969
8639	166.17	75.013	460.49	34.4	-6.4	28	2.6973	1573.8	615.99	968.95	...	1653.0	218.68	3118.3	313.98	511.23	630.14	47.901	51.847	50.052	47.623
6417	164.04	79.930	461.29	34.4	-6.4	28	2.6682	1555.8	616.01	969.05	...	1638.3	212.68	2885.5	312.73	508.83	626.67	47.922	48.169	49.015	47.011
9588	165.04	79.501	461.00	34.4	-6.4	28	2.6834	1563.7	615.99	969.05	...	1638.8	211.12	2992.5	314.42	509.86	628.05	46.394	49.674	48.009	46.942

	F3	Tatm	T1	P4	deltaP	P6	Fair	T3	T2	Tr	...	FLCO	FSlurry	FReflux	Tfra	T10	T20	V9	V8	V10	V11
948	164.99	79.501	460.71	34.4	-6.4	28	2.6826	1678.9	616.00	969.04	...	1647.9	207.77	2995.1	314.42	509.86	628.01	46.382	49.717	48.940	47.463
385	164.85	78.924	460.63	34.4	-6.4	28	2.6780	1588.0	616.00	969.00	...	1639.8	216.51	2966.8	313.62	509.62	627.88	47.285	49.381	49.306	47.017
887	164.65	79.705	461.03	34.4	-6.4	28	2.6724	1674.3	616.00	968.95	...	1632.7	223.99	2952.5	313.99	509.38	627.72	46.854	49.076	49.828	46.632
696	164.63	80.014	460.81	34.4	-6.4	28	2.6769	1613.9	616.01	969.03	...	1646.1	217.44	2995.2	314.84	509.73	628.09	45.900	49.646	50.052	47.372
944	165.04	79.551	460.68	34.4	-6.4	28	2.6831	1679.4	615.99	969.04	...	1646.3	206.67	2993.9	314.41	509.86	627.98	46.371	49.698	48.797	47.374

	count	mean	std	min	25%	50%	75%	max
F3	1440.0	164.964931	1.705031e-01	164.480000	164.840000	164.970000	165.080000	165.520000
Tatm	1440.0	78.342074	1.495206e+00	75.014000	77.206250	78.782000	79.699250	80.057000
T1	1440.0	460.921306	3.773500e-01	459.880000	460.660000	460.910000	461.190000	461.930000
P4	1440.0	34.400000	8.884870e-13	34.400000	34.400000	34.400000	34.400000	34.400000
deltaP	1440.0	-6.400000	1.732550e-13	-6.400000	-6.400000	-6.400000	-6.400000	-6.400000
P6	1440.0	28.000000	0.000000e+00	28.000000	28.000000	28.000000	28.000000	28.000000
Fair	1440.0	2.679885	3.071059e-03	2.671800	2.677700	2.680100	2.682000	2.689500
T3	1440.0	1631.535556	4.738479e+01	1558.900000	1584.475000	1670.550000	1676.725000	1686.400000
T2	1440.0	615.999743	7.034361e-03	615.960000	616.000000	616.000000	616.000000	616.020000
Tr	1440.0	968.999750	3.104291e-02	968.910000	968.980000	969.000000	969.020000	969.110000
Treg	1440.0	1250.001528	5.095774e-02	1249.900000	1250.000000	1250.000000	1250.000000	1250.100000
Lsp	1440.0	29.653148	9.402505e-02	29.376000	29.586000	29.655000	29.712000	29.906000
Tcyc	1440.0	1255.279028	5.020209e-02	1255.200000	1255.200000	1255.300000	1255.300000	1255.400000
Tcyc - Treg	1440.0	5.278568	3.786855e-02	5.187000	5.250200	5.280150	5.306700	5.388200
Cco,sg	1440.0	29881.456250	4.867664e+01	29737.000000	29846.000000	29879.500000	29917.250000	30009.000000
Co2,sg	1440.0	0.012471	1.692165e-04	0.012067	0.012344	0.012476	0.012599	0.012967
P5	1440.0	24.900000	6.752501e-13	24.900000	24.900000	24.900000	24.900000	24.900000
V4	1440.0	46.218401	3.991914e-01	45.335000	45.914250	46.324500	46.565250	46.835000
V6	1440.0	24.783983	1.008298e-01	24.532000	24.708000	24.797000	24.866250	25.033000
V7	1440.0	54.577811	6.263034e-02	54.413000	54.534000	54.582000	54.621000	54.773000
V3	1440.0	46.982208	1.595724e-02	46.937000	46.971000	46.982000	46.993000	47.025000
V1	1440.0	58.694293	5.779836e-01	57.569000	58.161750	58.781500	59.194000	59.838000
V2	1440.0	45.315695	5.303164e-02	45.177000	45.283000	45.317000	45.350000	45.481000
Frgc	1440.0	49572.277083	6.081520e+01	49407.000000	49529.000000	49576.000000	49614.000000	49765.000000
Fsc	1440.0	49572.236806	6.126673e+01	49411.000000	49529.000000	49577.000000	49614.000000	49764.000000
ACAB	1440.0	280.687549	1.405517e+00	277.550000	279.710000	281.060000	281.910000	282.860000
AWGC	1440.0	204.330486	2.734571e+00	198.270000	202.257500	205.050000	206.730000	208.440000
F5	1440.0	2016.612847	1.985887e+01	1977.900000	1998.300000	2019.600000	2033.800000	2055.900000
F7	1440.0	3735.767917	5.533354e+00	3722.500000	3731.800000	3735.800000	3739.800000	3752.000000
Fsg	1440.0	160.793132	1.845920e-01	160.310000	160.660000	160.810000	160.920000	161.370000
FV11	1440.0	28081.818750	3.012223e+02	27411.000000	27854.250000	28163.000000	28343.000000	28543.000000
P1	1440.0	14.637990	1.015644e-04	14.637000	14.638000	14.638000	14.638000	14.638000
P2	1440.0	35.044535	2.357686e-02	34.995000	35.026000	35.040000	35.063000	35.101000
FLPG	1440.0	3032.567014	4.823743e+01	2926.000000	2995.775000	3045.250000	3075.000000	3105.800000
FLN	1440.0	3921.324236	4.809104e+01	3852.500000	3878.700000	3909.200000	3958.325000	4029.600000
FHN	1440.0	708.488417	4.016996e+00	696.510000	705.877500	708.540000	710.872500	718.770000
FLCO	1440.0	1642.707361	4.562635e+00	1630.400000	1639.400000	1642.500000	1646.100000	1654.900000
FSlurry	1440.0	214.301500	4.559457e+00	201.700000	210.787500	214.325000	217.742500	225.080000
FReflux	1440.0	2977.411250	2.315561e+01	2923.500000	2960.100000	2982.000000	2994.925000	3029.300000
Tfra	1440.0	313.424194	1.300492e+00	310.550000	312.430000	313.760000	314.590000	315.290000
T10	1440.0	509.775236	1.368354e-01	509.380000	509.680000	509.770000	509.870000	510.130000
T20	1440.0	628.078847	1.482783e-01	627.680000	627.990000	628.080000	628.180000	628.400000
V9	1440.0	47.635750	1.609722e+00	45.383000	46.211750	47.225500	48.851500	51.273000
V8	1440.0	49.591987	2.162617e-01	49.074000	49.419000	49.595000	49.753000	50.139000
V10	1440.0	49.332665	5.618536e-01	47.652000	48.962000	49.339000	49.663500	50.769000
V11	1440.0	47.171890	2.516454e-01	46.498000	46.986000	47.158000	47.356000	47.845000

Feed Preheater Furnace tubes fouling¶

Introduction¶

Data Preprocessing¶

Exploratory Data Analysis (EDA)¶

Anomaly Detection Techniques¶

Data Cleaning, Feature Engineering, Predictive Modeling¶

Testing the model on Varying feed flow rate.¶

Testing the model on abnormal dataset.¶

Visualization¶

Conclusion¶

Future Work¶

*Feed Preheater Furnace tubes fouling*¶

Introduction¶

Data Preprocessing¶

Exploratory Data Analysis (EDA)¶

Anomaly Detection Techniques¶

Data Cleaning, Feature Engineering, Predictive Modeling¶

Testing the model on Varying feed flow rate.¶

Testing the model on abnormal dataset.¶

Visualization¶

Conclusion¶

Future Work¶

Feed Preheater Furnace tubes fouling¶